Quadratic Equation Application Word Problem : Maximizing Rectangular Area
Anne decides to start a vegetable garden and buys 100m of wire netting to fence off a rectangular area from the rabbits.Assume that Anne uses an existing fence as one side of the rectangle, and the 100m netting for the other three sides.
- If x is the width of the rectangular garden, write an expression for the length of the garden in terms of x and find the formula for the area A of the garden in terms of x alone.
- Draw a graph of the area function including an appropriate domain and find at what value of x is the area a maximum
- What dimensions should Anne make her vegetable garden to achieve the maximum area?
Solution Summary
Rectangular area is maximized and a graph is sketched. The solution is detailed and well presented.
A field is to be marked off in the shape of a rectangle, with one side formed by a straight river. If 100 feet is available for fencing, find the dimensions of the rectangle of maximum possible area.
1. Determine the quadratic function F whose graph is given:
The vertex is (3, -11) an the y-intercept is -2.
2. A man has available 2800 yards of fencing and wishes to enclose a rectangulararea.
4. Express the area A of the rectangle as a function of W of the rectangle.
8. For what value of W is the area largest?
Congratulations, you have just purchased your first house. Unfortunately, the builder forgot to put a fence around the property and you must now put a fence up so that you can let your pet out in the backyard, without fear of it running away.
(My pet would be a large dog such as a Mastiff).
You want to fence in a rectangul
Application Assignment #4
(QuadraticEquations)
Answer the following questions. Use Equation Editor to write mathematical expressions and equations. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting.
Part 1
Mrs. Thom
1. Solve by factoring: 2x^2 + 5x = 3
3. Solve by using the square root property: 3x^2 = 16
6. Solve by completing the square: 2x^2 - 3x - 4 = 0
7. Solve using the quadraticequation: 2x^2 - 3x - 4 = 0
(See attachment for all questions)
Write a wordproblem involving a quadratic function. How would you explain the steps in finding the solution to someone not in this class?
Problem:
My garden is 18 ft long and 15 ft. wide. I like to decrease the length by x feet and increase the width by the same number of feet. The equation A = (18-x)(15+x) = 270 + 3x - x^
A.
A rectangular garden is to be fenced in and divided into three parallel sections. the fencing for the boundary costs $20 per foot whereas fencing for the dividing fences costs $5 per foot. Consider the problem of finding the dimensions of the largest garden possible if the gardner can spend $2000 for the fencing. Find the va
Given, this partial equation, how do I complete it?
Finding the width I used this equation - L= 2W + 2
I know my length is 10 feet. 10 = 2W + 2
10 -2 ft = 2W +2 - 2
8 = 2W
8/2 = 2W/2
Please see the attached file - Don't mind the graphing portion, work what can be worked. I have to input answers not write out the whole equation.
7. Find the vertex, line of symmetry, and the maximum or minimum value of a quadratic function, and graph the function.f(x) = -x +6x +2
The vertex is
8. Find the vertex,lin
